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Complex numbers are often used when dealing with alternating current (AC) circuits. In the equation $V = IZ$, $V$ is voltage, $I$ is current, and $Z$ is a value known as impedance. If $V = 1-i$ and $Z=1+3i$, find $I$. Express your answer as a complex number in the form $a+bi$, where $a$ and $b$ are real numbers.

 Jun 22, 2019
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\(V = IZ\\ 1-i = I(1+3i)\\ I = \dfrac{1-i}{1+3i}\\ I = \dfrac{(1-i)(1-3i)}{(1+3i)(1-3i)}\\ I = \dfrac{-2-4i}{10}\\ I = -\dfrac{1}{5} -\dfrac{2}{5}i\)

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 Jun 22, 2019

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